Catmull–Rom Curves
Three interactive canvases compare Catmull–Rom curve interpolation under uniform, chordal, and centripetal parameterization, using the same seven control points rendered as white polylines. Each canvas overlays a static image of the curve, while a slider adjusts the alpha parameter via the `data-alpha` attribute. The code uses `d3.shape.line` with the `"catmull-rom"` interpolator and a Canvas 2D context to draw the paths. The example is based on Yuksel et al.’s research on parameterization effects, highlighting how each method handles overshoot and intersections differently.
AI-generated descriptionCubic Catmull–Rom curves with (b) uniform, (c) chordal and (d) centripetal parameterization. From Yuksel et. al: “Uniform parameterization overshoots and often generates cusps and intersections within short curve segments, while chord-length parameterization exhibits similar behavior for longer curve segments. Centripetal parameterization is the only one that guarantees no intersections within curve segments.”